Cryptographic methods and devices for pseudorandom generation, encrypting data, and cryptographically hashing a message
The invention relates to the general field of digital security and more particularly cryptography. In particular it proposes a device and a method of encrypting a sequence of data. The invention also relates to a cryptographic device (1) and a cryptographic method of generating a pseudorandom data sequence (13) and their favored use in the field of digital security, in particular for encrypting and decrypting data and for cryptographically hashing messages.
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Description
This Application is a U.S. National Stage Application under 35 U.S.C. §371 of International Application PCT/EP2008/056889 filed Jun. 4, 2008, which designated the U.S. and was not published in English, and claims the foreign filing date benefits and priority from European Application 07301086.0, filed Jun. 5, 2007, and the complete disclosure of each said application is incorporated herein by reference.
TECHNICAL FIELD OF THE INVENTION
The invention relates to the general field of digital security and more particularly to cryptography.
It proposes inter alia a device and a method for symmetrically encrypting a data sequence. The invention also relates to a cryptographic device and a cryptographic method for generating a pseudorandom data sequence and to their favored use in the field of digital security, in particular for encrypting and decrypting data and for cryptographically hashing messages.
BACKGROUND OF THE INVENTION
Encrypted data is systematically exchanged at a high bit rate using symmetrical encryption algorithms.
The efficacy of a symmetrical encryption algorithm is evaluated on the basis of its resistance to cryptanalysis, which depends on the complexity of the processing applied to the information to be encrypted, the absence of weaknesses, and its resistance to a brute force attack, which depends on the size of the encryption key.
Moreover, the efficacy of symmetrical encryption also depends on its speed of execution. The bit rate at which the encryption algorithm operates must be higher than the maximum bit rate of the application concerned for information that is to be encrypted/decrypted.
Accordingly, for a high bit rate application, secure solution integrators are faced with a dilemma when choosing an encryption algorithm because, with increase in the bit rates of information to be processed and for constant calculation power, the time available for processing information decreases, leading to compromises in terms of cryptanalysis resistance.
Prior art stream encryption mechanisms that perform symmetrical encryption encrypt data continuously, in the course of successive iterations, and can be used advantageously when the data bit rates are high and/or when it is essential to encrypt/decrypt information in real time.
Referring to
These stream encryption methods, although extremely fast in a hardware implementation because of their simplicity and the small number of instruction sets used, have several severe limitations that are generally accepted because they are a direct corollary of the high bit rates specified.
Firstly, the pseudorandom generators used by these stream encryption methods are generally based on the use of linear or nonlinear shift registers. Used as such, these shift registers have serious cryptographic shortcomings. To render the pseudorandom behavior of the generator cryptographically acceptable, it is known to combine the shift registers with one another using combination functions. The increase in the number of registers necessary to feed these combination functions and the complexity of the combination functions themselves significantly impact on the number of components required in a hardware implementation and limit the speeds of execution of the pseudorandom generation algorithm and the encryption method.
Moreover, these pseudorandom generators generate only a very limited number of output bits at a time (typically one bit, possibly 8 or 16 bits). Consequently, the number of bits encrypted on each iteration of the stream encryption method is also very limited and does not necessarily meet the real requirements of the applications having data protected by the method.
To alleviate these drawbacks, stream encryption mechanisms that use block encryption algorithms for the pseudorandom generation can be used. An example of a stream encryption mechanism using a block encryption algorithm in cipher feedback (CFB) mode is represented in
Furthermore, the design of the stream encryption mechanisms described above, based on applying an exclusiveOR operation to an output bit of the pseudorandom generator and to a bit of the message to be encrypted, renders the pseudorandom generator directly observable in the context of standard cryptanalysis and commandable in CFB mode as shown in
Consequently there exists a need for a solution for fast generation of cryptographically secure pseudorandom sequences of vectors of any predefined size, an encryption/decryption solution that is free of such drawbacks of observability and commandability of the pseudorandom generator, and a guaranteed high level of digital security, whilst ensuring simple and efficient implementation (notably in terms of execution speed) both in hardware and in software.
OBJECT AND SUMMARY OF THE INVENTION
A first aspect of the invention addresses this need by proposing a cryptographic method of generating a pseudorandom data sequence formed by a succession of values of a state vector of size k generated iteratively from an initial value of the state vector. According to the invention, during each iteration of the cryptographic method, in order to generate a current value of the state vector for that iteration, a predetermined number d of permutations of size k1 greater than or equal to k are applied successively to a provisional vector of size k1 including at least one first intermediate vector of size k formed from at least one section of a preceding value of the state vector generated in a preceding iteration. Each permutation is associated respectively with a distinct bit of a permutation key of size d and chosen as a function at least of the value of that bit, said permutation key being the result of selecting d distinct bits from the k bits of the first intermediate vector. The current value of the state vector is then obtained from at least one section of the result vector of this application step.
The description below relates to binary data and binary vectors, i.e. data and vectors whose components are bits. Thus a vector of size t is a vector consisting of t bits.
In the sense of the invention, the expression “vector V_{a }comprising a vector V_{b}” means a vector V_{a }that includes among its components all of the components of the vector V_{b }(consecutively or not, in the same order or in any order). For example, if a vector V_{b}=(1,0,0,1) and a vector V_{a}=(0,1,V_{b}) are considered, the vector V_{a }is a vector including the vector V_{b }and equal to V_{a}=(0,1,1,0,0,1).
Moreover, in the sense of the invention, the expression “section of a vector of size t” means a set of j bits of that vector occupying particular positions in that vector, j lying in the range 1 to t (1≦j≦t). Thus a section of size t of a vector of size t refers to the vector itself.
The particular positions occupied by the j bits of the section are preferably predetermined and fixed (for example a section consisting of the first j bits of a vector or a section consisting of the last j bits of a vector). However, they could equally be determined, for example, as a function of the value of a section of the vector whose bits occupy predetermined and fixed positions, and because of this not necessarily fixed in time.
Thus on each iteration the invention produces from the current value of the generated state vector any number of pseudorandom bits less than or equal to the size k of the state vector, k being a parameter taking any value (there is no theoretical limitation on the values of k that can be considered). The invention can therefore be easily used in diverse applications requiring pseudorandom vectors of varying size (not necessarily limited to only one bit), adapting to the requirements of the target application.
Moreover, the invention proposes to generate a pseudorandom data sequence iteratively using a permutation function made up of d permutations and with parameters set (or parameterized) by a permutation key that is itself pseudorandom because it is extracted from a pseudorandom vector. Each of the d permutations is chosen from a predefined pair of permutations (which pair can vary from one permutation stage to another or remain the same for all stages), as a function at least of the value of the bit of the associated permutation key with. The size d of the permutation key (d≦k) is a parameter and can in particular be made relatively large so as to ensure better mixing of the permutated data.
The permutation function used in the invention is advantageously a oneway function. As known in itself, a oneway function can easily be calculated in one direction, but is difficult or even impossible to invert in a reasonable time (i.e. with reasonable complexity).
The permutation function used in the invention is such that calculating an output data vector as a function of an input data vector requires the evaluation of k1 equalities each with one explicit term. In contrast, on attempting to calculate an input data vector as a function of an output data vector, it is necessary to solve a multivariate system (i.e. one for which each term is a combination of a plurality of unknowns) consisting of k1 equations each comprising 2^{d }terms in d unknowns. Thus it is clear that such a system of equations cannot be solved simply because the number of terms in each equation is very much greater than the number of equations, and in particular is extremely large for high values of d.
Moreover, this number increases as the iterations proceed, i.e. the system is “selfcomplicating”. In hardware terms, the consequence of this is that the set of equations to be solved cannot be written down and stored physically, in particular for large key sizes. For example, for a permutation key of size d=k=256, a multivariable system of 256 unknowns comprising 256 equations each with 2^{256 }terms must be solved on the first iteration.
The oneway function implemented in the invention is therefore particularly difficult to invert and robust to brute force attacks and to cryptanalysis (its mathematical complexity is very high), while offering relatively uncomplicated implementation, notably in terms of wiring, through the use of permutations. It can therefore be implemented using a lowlevel architecture, is compact because it requires few components, and therefore offers fast execution in a hardware or software implementation.
To enhance the quality of the generated pseudorandom sequence and to obtain a high quality of mixing, the d permutations of size k1 considered could advantageously be chosen from predefined permutation pairs P0, P1 (P0 designating a permutation associated with a bit when that bit is equal to 0 and P1 designating a permutation associated with a bit when that bit is equal to 1) satisfying at least one of the following conditions:

 for each bit of the key, the permutation obtained by respective composition of P0 and P1 and the permutation obtained by respective composition of P1 and P0 are different at all points;
 an identical pair of permutations P0 and P1 at all points different is used for each of the d stages of the oneway function (a stage corresponding to the application of a permutation);
 a pair of permutations P0 and P1 individually different at all points from the identity permutation is used for each of the d stages of the oneway function; in this way, each bit of the permutation key affects all the bits of the input data to be permutated.
Using identical permutation pairs in each stage has the advantage of reducing the hardware complexity of the pseudorandom generation method of the invention. Only two modules, respectively corresponding to the two permutations P0 and P1, need to be implemented in hardware. To implement the invention these modules can then be used several times in succession or d identical modules could be used for each permutation (i.e. 2d modules in all).
However, these assumptions are in no way limiting on the invention, as other permutations can be considered. In particular, it is possible to consider distinct permutation pairs (P0, P1) at the different permutation stages (i.e. for the distinct bits of the key).
In a different implementation, the provisional vector further includes the vector obtained by complementing each bit at 1 of the first intermediate vector. Thus, for example, if V_{prov }designates the provisional vector and V_{int1 }designates the first intermediate vector, then it can be taken that:
V_{prov}=(
in which
This produces a strict avalanche effect, regardless of the value of d; i.e. modifying a single bit of the first intermediate vector V_{int1 }statistically affects the value of half the bits of the vector resulting from application of the oneway function and used in the construction of the current value of the state vector. The consequence of this is to limit the negative impact linked to the use of a first intermediate vector that is sparse (i.e. of low Hamming weight) and to improve the resistance of the cryptographic pseudorandom generation method of the invention to hardware attacks. The spread achieved within the process is thus excellent, which constitutes a noteworthy cryptographic quality.
Moreover, the provisional vector obtained in this way has a constant Hamming weight equal to k, whatever the value of the first intermediate vector. Also, in a hardware implementation, executing the oneway function, regardless of the values of d and V_{int1}, has absolutely constant electrical power consumption. In each stage of permutation of the oneway function there is a constant number of bits at 1 and the activation of each stage of the oneway function activates an identical number of logic gates whether the bit of the key concerned is at 0 or at 1. The oneway function of the invention is therefore also insensitive to hardware attacks based on power consumption analysis.
In another variant implementation of the invention, the provisional vector can be taken as equal to the first intermediate vector (k1=k).
In one particular implementation of the invention, the current value of the state vector is the result of applying an exclusiveOR operation to said section of the vector resulting from the application step and the preceding value of the state vector.
This implementation increases the mathematical complexity of the process of generating successive pseudorandom values of the state vector. The exclusiveOR operation loses all information concerning the weight of the initial value of the state vector, the Hamming weight of the state vector thus being modified as the iterations proceed.
In one particular implementation of the invention, the provisional vector and the permutation key are the same size, which is equal to the size of the first intermediate vector.
In this embodiment the description refers to a square oneway function, as opposed to a rectangular oneway function, in which the permutation key is of size d (d≦k) different from the size k1 (k1≧k) of the provisional vector to which the oneway function is applied.
In another implementation of the invention, the above cryptographic method of generating a sequence of pseudorandom data is such that each iteration further includes, before the application step, a step of obtaining a current intermediate value calculated from the preceding value of the state vector and an input data block, the first intermediate vector being formed by the preceding value of the state vector in which a section has been replaced by the current intermediate value.
Thus the pseudorandom data sequence generated by means of the invention has no particular period and follows no preestablished cycle as a function only of the initial value of the state vector. The current value of the state vector depends on the initial value of the state vector and of the whole of the input data sequence applied. This ensures dynamic evolution of the pseudorandom data sequence.
The method conforming to this way of generating a pseudorandom data sequence has highlyadvantageous properties making it a potential candidate for numerous cryptographic security applications.
In particular, the invention is also directed to using such a cryptographic method of generating a pseudorandom data sequence in a method of cryptographically hashing a message to generate a digest of the message, the latter including a predetermined number M of data blocks used in turn as input data blocks for calculating the current intermediate value during successive iterations of the cryptographic method of generating a sequence of pseudorandom data in order to generate M values of the state vector. The digest of the message is then obtained from the latest value of the state vector generated in this way.
The hashing method used in this way has all the advantages of the pseudorandom generation method of the invention, in particular in terms of robustness and simplicity of implementation.
Moreover, the invention is also directed to the use of such a cryptographic method of generating a pseudorandom data sequence in a method of encrypting an input data sequence, as described in more detail below.
A second aspect of the invention relates to a method of symmetrically encrypting an input data sequence, in which, on the basis of an initial value of a state vector and a succession of input words forming said input sequence, a succession of values of said state vector and a succession of output words are generated iteratively, each iteration including the following steps:

 an encryption step in which a current output word for the iteration is calculated by a reversible application depending on a current input word and said preceding value of the state vector generated in the preceding iteration; and
 a pseudorandom generation step in which a current value of the state vector for said iteration is calculated by a noninvertible application depending at least on said preceding value of the state vector;
said method being characterized in that:

 said reversible application includes at least first and second secret key functions, said secret keys being generated from at least one section of the preceding value of the state vector; and
 said noninvertible application further depends on a current intermediate value depending on the preceding value of the state vector and the current input word and being isolated from the input words, respectively from the output words, by means of said first secret key function, respectively said second secret key function.
In the sense of the invention, the expression “vector isolated from the input and output words” refers to a vector that is not accessible using the input and output words, i.e. not commandable and not observable by means of those words. By definition:

 a system characterized by an input, a state vector and an output is noncommandable if the state vector cannot be brought to a predetermined value by applying a finite input sequence;
 a system characterized by an input, a state vector and an output is nonobservable if the value of the state vector at a given time cannot be deduced from a finite number of observations of the output sequence.
As the person skilled in the art knows, the initial value of the state vector in a symmetrical encryption process is secret. By recurrence, if the preceding value of the state vector is both noncommandable and nonobservable, then the current intermediate value used to calculate the current value of the state vector in the encryption method of the invention is itself noncommandable and nonobservable. Consequently, the current state vector obtained is also noncommandable and nonobservable, i.e. isolated from the input and output words. This prevents direct observation of the value of the state vector or reconstruction or piloting of the succession of values of the state vector. Moreover, it is not necessary to modify the initial value of the state vector to avoid information leaking (for example a first encrypted message ⊕ a second encrypted message=a first message in clear ⊕ a second message in clear).
It is particularly advantageous that the encryption methods of the invention can be used interchangeably to encrypt a message in clear or to decrypt an encrypted message, the input data sequence being taken sometimes as equal to the message in clear and sometimes as equal to the encrypted message. Decryption is performed by the operations that are the reverse of those of encryption, which is of great benefit from the hardware implementation point of view. Also, in the remainder of the description, the expression “encryption method of the invention” refers to a method of encrypting and/or decrypting an input data sequence.
Thus it is possible to encrypt/decrypt an input data sequence formed by a succession of input words of any size with an optimum execution speed at the same time as ensuring simple and efficient implementation in hardware and in software.
The successive values of the state vector depend on the initial value of the state vector and the whole of the input data sequence. As a result, the state vector has a dynamic evolution that is noncommandable and nonobservable. This ensures highly secure encryption/decryption.
In one particular implementation, the first secret key function and/or the second secret key function includes at least one exclusiveOR operation with parameters set by at least one section of the secret key of that function, i.e. by at least one section of the preceding value of the state vector.
In one particular implementation of the invention, each state vector is of size k and, during the pseudorandom generation step, to calculate the current value of the state vector, there are applied successively to a provisional vector of size k1 greater than or equal to k comprising at least one first intermediate vector of size k formed from a section of the preceding value of the state vector and from the current intermediate value a predetermined number d of permutations of size k1 each associated with a respective distinct bit of a permutation key of size d chosen as a function at least of the value of this bit, said permutation key being the result of selecting d distinct bits from the k bits of the first intermediate value and the current value of the state vector being obtained from at least one section of the vector resulting from this application step.
Thus the encryption method of the invention has the same advantages as the pseudorandom generation method of the invention described above. It can moreover include in different embodiments the different variants proposed above for the pseudorandom generation method of the invention.
Using such a pseudorandom generation method in a stream encryption algorithm has the advantage of guaranteeing a high degree of digital security at the same time as ensuring simple and efficient implementation (in particular in terms of execution speed) in hardware and software.
In a particularly advantageous variant of the invention, the input and/or output words comprise a plurality of bits variable as a function of the iteration. The state vector can then include a section indicating this number of bits variable on each iteration.
The state vector being a pseudorandom variable, the encryption method processes input words to be encrypted of variable size on each iteration, this size also varying in a pseudorandom manner as a function of the input data sequence and the initial value of the state vector. The state vector being isolated from the input and output words of the encryption method, it is impossible to determine which subdivision (in terms of size) has been effected at the level of the input words during the encryption method. This provides even better protection against cryptanalysis.
In this particular implementation of the invention, the pseudorandom generation step of each iteration can further include, when it is determined that said variable number of bits is zero from the current value of the state vector, the calculation by a noninvertible application dependent on the current value of the state vector of a new current value of the state vector replacing that current value of the state vector.
Thus the succession of values of the state vector is generated “empty” for as long as the size of the input or output words remains equal to 0 without interaction with the encryption step. In other words, the operations effected during the pseudorandom generation step are desynchronized from those effected during the encryption step, providing even more protection.
In one particular implementation of the invention:

 the pseudorandom generation step is a first pseudorandom generation step forming a current value of a first state vector;
 said first pseudorandom generation step is combined in parallel with at least one second pseudorandom generation step forming a current value of a second state vector; and
 the current value of the state vector is the result of applying an exclusiveOR operation to the current value of the first state vector and at least the current value of the second state vector.
Thus different pseudorandom state vectors are combined, which increases the mathematical complexity of successive pseudorandom generated data by producing increasingly large cycles.
In another implementation of the invention, the encryption step is a first encryption step in which there are calculated:

 a first current output word by a first reversible application depending on a first current input word and at least one first section of the preceding value of the state vector; and
 a first current intermediate value.
Moreover, the method further includes at least one second encryption step in which there are calculated:

 a second current output word by a second reversible application depending on a second current input word and at least one second section of the preceding value of the state vector; and
 a second current intermediate value;
 the current intermediate value used during the pseudorandom generation step including the first current intermediate value and at least the second current intermediate value.
Thus a plurality of signals can be multiplexed with the same state vector, which simplifies hardware or software implementation.
In another implementation of the invention, the encryption method further includes a step of cryptographically multiplexing at least two message blocks in clear to form at least two encrypted message blocks, each message block in clear corresponding to a succession of input words, and said at least two encrypted message blocks are ordered in each iteration as a function of a section of the preceding value of the state vector.
Thus the ordering or mixing on each iteration of the M encrypted blocks, combined or not, in transmission channels is pseudorandom and depends on the initial value of the state vector and the whole of the input sequences. Consequently, any modification in the input sequences modifies the mixing, thus providing optimum protection.
As described above, the invention proposes a pseudorandom generation method based on a oneway function that is robust to cryptanalysis and to brute force attacks, fast and of relatively uncomplicated hardware implementation.
Also, the invention further provides a cryptographic module adapted to generate a vector of output bits from a vector of input bits of size k1, including:

 means for forming a permutation key of predetermined size d by selecting d distinct bits from the bits of the input vector;
 means for associating with each bit of the permutation key a permutation of size k1 chosen as a function at least of the value of that bit; and
 means for applying successively to the input vector the d permutations of size k1 associated with the d bits of the permutation key to obtain said vector of output bits.
The cryptographic module of the invention advantageously uses the abovementioned oneway function.
Moreover, the invention also provides a cryptographic generator of a pseudorandom data sequence formed of a succession of values of a state vector of size k generated iteratively from an initial value of the state vector, said generator including means for using in each iteration to generate a current value of the state vector for said iteration:

 a cryptographic module as described above adapted to generate a result vector from a provisional vector of size k1 greater than or equal to k including at least one first intermediate vector of size k formed from at least one section of a preceding value of the state vector generated in a preceding iteration, said permutation key being of size d less than or equal to k; and
 means for obtaining the current value of the state vector from at least one section of the result vector.
In one embodiment, this generator further uses in each iteration:

 means for obtaining a current intermediate value calculated from the preceding value of the state vector and an input data block; and
 means for forming said first intermediate vector from the preceding value of the state vector in which a section has been replaced by the current intermediate value.
The invention further provides a device for encrypting an input data sequence adapted to generate iteratively from an initial value of a state vector and a succession of input words forming said input sequence, a succession of values of the state vector, and a succession of output words, said encryption device using in each iteration:

 encryption means adapted to calculate a current output word for said iteration by a reversible application depending on a current input word and a preceding value of the state vector generated in a preceding iteration; and
 a pseudorandom generator adapted to calculate a current value of the state vector for said iteration by a noninvertible application depending at least on the preceding value of the state vector.
According to the invention said encryption device is such that:

 the reversible application includes at least first and second secret key functions, the secret keys being generated from at least one section of the preceding value of the state vector; and
 the noninvertible application further depends on a current intermediate value depending on the preceding value of the state vector and the current input word and being isolated from the input words, respectively the output words, by means of said first secret key function, respectively said second secret key function.
In one embodiment, the pseudorandom generator of the encryption device of the invention is a cryptographic generator of a pseudorandom data sequence of the invention as described above.
In one particular embodiment of the invention, the encryption device is adapted to process input words and/or output words comprising a number of bits variable as a function of the iteration and further includes means for determining the variable number of bits in each iteration from a section of the state vector. In this embodiment the pseudorandom generator of the encryption device can further include means for calculating a new current value of the state vector replacing the current value of the state vector by a noninvertible application depending on the current value of the state vector when it is determined from the current value of the state vector that said variable number of bits is zero.
In another embodiment, the encryption device further includes a device for cryptographically multiplexing at least two message blocks in clear to form at least two encrypted message blocks, each message block in clear corresponding to a succession of input words, and said at least two encrypted message blocks are ordered in each iteration as a function of a section of the preceding value of the state vector.
The invention further provides a cryptographic hashing device adapted to generate a digest from a message including a predetermined number M of data blocks, said hashing device including:

 a cryptographic generator according to the invention as described above, generating a succession of M values of a state vector in M successive iterations;
 means for, in each of the M iterations:
 calculating the current intermediate value for that iteration from a current data block of the message and the preceding value of the state vector generated by the cryptographic generator; and
 supplying the current intermediate value to the cryptographic generator; and
 means for obtaining the digest of the message from the latest value of the state vector generated by said generator.
Moreover, it should be noted that, in one particular embodiment of the invention, the cryptographic generator and/or the encryption device and/or the cryptographic hashing device of the invention can be implemented by one or more dataprocessing systems conventionally including a central processor unit controlling by signals a memory, an input unit and an output unit interconnected by data buses.
Thus the invention also provides a computer program including program code instructions for executing a cryptographic method of generating a pseudorandom data sequence having any of the above features, a computer program including program code instructions for executing an encryption method having any of the above features, and a computer program including program code instructions for executing a cryptographic hashing method having any of the above features when those programs are loaded into and executed in a computer or dataprocessing system.
These computer programs can be stored on computerreadable media and can be executable by a microprocessor.
They can use any programming language and take the form of source code, object code or a code intermediate between source code and object code, such as a partiallycompiled form, or any other desirable form.
The invention also provides a computerreadable information medium containing instructions of a computer program as described above.
BRIEF DESCRIPTION OF THE DRAWINGS
Other features and advantages of the invention emerge on reading the description given below by way of nonlimiting illustration and with reference to the appended drawings, in which:
DETAILED DESCRIPTION OF EMBODIMENTS
Preliminary Note and Notation
In a manner that is particularly advantageous, the invention proposes a permutation function P that is configurable (or parameterizable), i.e. a function having parameters that can be set, which function can be used in diverse cryptographic applications, as described below, in particular for pseudorandom generation, for encrypting/decrypting data, and for cryptographically hashing a message.
This permutation function P can have its parameters set as a function of the size of the data to which it is applied and has its parameters set by a socalled permutation key. Thus the following notation convention is used:
S=P(E,C)
to designate that the permutation function P as with parameters set by the permutation key C is applied to input data E to obtain output data S.
Generally speaking, for input data E of size e and a permutation key C of size p less than or equal to e, the permutation function P is the result of applying p successive permutations of size e to the input data E, each permutation being associated with one bit of the permutation key C and chosen as a function at least of the value of that bit.
For example, there is associated with each bit of the permutation key, i.e. with each permutation stage of the permutation function, a permutation P0 if that bit is at 0 and a permutation P1 if that bit is at 1.
The same pair of permutations (P0, P1) can be considered at the various stages of the permutation function P. These permutations P0 and P1 are then preferably defined as different from each other at all points and each individually different at all points from the identity permutation. However, these assumptions are not under any circumstances limiting on the invention, and different pairs of permutations can be considered at each stage of the permutation function, or other conditions applied to the permutations P0 and P1, for example that the permutation obtained by composing the permutations P0 and P1 must be different at all points from the permutation obtained by composing the permutations P1 and P0.
The permutation function P has different properties according to the permutation key considered.
Thus if the permutation key C is formed from data independent of the input data to which the permutation function P is applied, a bijective (or key permutation) function is obtained, i.e. the function P is invertible provided that the value of the permutation key is known, i.e. that to a value of the input data of the function P with parameters set by this key there corresponds only one value of the output data.
This property of the permutation function P is considered in particular in certain embodiments relating to an encryption/decryption device and a cryptographic hashing device of the invention.
If the permutation key C is formed from input data E to which the permutation function P is applied (in other words, if the permutation key depends on the whole or part of the input data E), a oneway function is obtained, i.e. the function P is noninvertible, in other words is easy to calculate in one direction but difficult or even impossible to invert in a reasonable time (i.e. with a reasonable complexity).
Such a permutation function with parameters set in this way (i.e. with a permutation key depending on the input data to which the permutation function is applied), and a fortiori a oneway function based on such a permutation function, has never been proposed or used in the prior art.
This property of the permutation function P is notably considered for a cryptographic module and a cryptographic generator of a pseudorandom data sequence (pseudorandom generator) in different embodiments of the invention.
In the remainder of the description, to distinguish between applications of the permutation function P as a function of its properties, the expression “surjective permutation means” refers to the means implementing the permutation function P when it is a oneway function (also referred to below for simplification as “surjective permutation”). Consequently, surjective permutation must be understood as noninvertible (i.e. nonbijective), because it is used in the context of a oneway, i.e. noninvertible, function and in the context of that oneway function, different input data E1, E2, . . . can have the same output S (for example, S=P(E1, E1)=P(E2, E2)= . . . , with E1≠E2≠, . . . ).
Similarly, the expression “bijective permutation means” refers to the means implementing the permutation function P when it is a bijective function, in other words a bijective key permutation (also referred to below for simplicity as “bijective permutation”).
The features of and means for implementing the permutation function P are explained in more detail below, in particular with reference to
PseudoRandom Generation Method and Generator
The pseudorandom generator 1 includes calculation means 5 which, starting from an initial value V_{0 }of a state vector V, form the pseudorandom data sequence 3 by iterative generation of a succession of values V_{0}, . . . , V_{n1}, V_{n}, . . . of the state vector. Note that V_{n }corresponds to the value taken by the state vector V_{n }on the n^{th }iteration. The same convention is used in a similar way for the other variables.
The state vector V comprises a particular number k of bits (i.e. it is a vector of size k, where k is an integer greater than or equal to 1).
On each iteration n of the pseudorandom generation process, the calculation means 5 calculate a current value Vn of the state vector V using a noninvertible application depending on a preceding value V_{n1 }of the state vector. This noninvertible application is based on a oneway function with parameters set by a permutation key of size d≦k.
In the example envisaged here, the state vector is advantageously fed on each iteration n with a current intermediate value X_{α }calculated by another application, for example the application AT, which can depend on the previous value V_{n1 }of the state vector and a current input word U_{n }belonging to an input data sequence (an input data block in the sense of the invention). In the example described here, the input words U_{n }comprise a particular number m of bits (words of size m), where m is an integer greater than or equal to 1. The current intermediate value X_{α }comprises m bits (vector of size m).
Examples of the application AT are described below, in particular with reference to
Referring to
On the first iteration, the pseudorandom generator 1 calculates a first value V_{1 }of the state vector V as a function of a first input word U_{1 }(using the current intermediate value X_{α}) and the initial value V_{0 }of the state vector.
By extension, on the n^{th }iteration, the pseudorandom generator 1 calculates a current value V_{n }of the state vector V as a function of a current input word U_{n }(using the current intermediate vector X_{α}) and the preceding value V_{n1 }of the state vector.
In this example, the pseudorandom generator 1 includes transmission means 321, reception means 323, and calculation means 325a, 325b, 325c, 326, and 327.
On each iteration (for example on iteration n), the transmission means 321 send the application AT the preceding value V_{n1 }of the state vector. The reception means 323 receive from the application AT the current intermediate value X_{α}.
First calculation means 325a replace a section X_{n1 }of size m of the preceding value V_{n1 }of the state vector with the current intermediate value X_{α }to form a current value of a first intermediate state vector V_{int1}.
In the example described here, second calculation means 325b form a current value of a provisional vector V_{prov }of size k1 greater than or equal to k from the current value of the first intermediate state vector V_{int1 }and the current value of the complementary vector, written
Here the current value of the provisional vector obtained in that way is:
V_{prov}=(
The provisional vector is then of size k1=2k.
Alternatively, this provisional vector can be equal to V_{int1 }(i.e. the second calculation means 325b can be dispensed with) and is then of size k. An embodiment corresponding to such an option is represented in
The current value of the provisional vector is then supplied to third calculation means 326 comprising surjective permutation means 326a adapted to apply a oneway function to the current value of the provisional vector to produce the current value of a result vector V_{res}. The oneway function applied by the surjective permutation means 326a is based on the configurable permutation function P described above with its parameters set by a permutation key C of predetermined size d (i.e. p=d) less than or equal to k. Here the choice made is d=k.
The current value of the permutation key C of the oneway function is formed by formation means 326b from the current value of the first intermediate state vector. In the example described here, the current value C is taken as equal to the current value of the first intermediate state vector, C=V_{int1}.
Below, for simplicity, C and the term “key” are used interchangeably for the current value of the permutation key for iteration n and the permutation key itself (i.e. the random variable).
Alternatively, in another embodiment of the invention, the size of the key d can be strictly less than k. The permutation key C is then formed by the means 326b selecting d distinct bits, consecutive or otherwise, from the k bits of the first intermediate vector V_{int1}, the positions of the selected d bits preferably being predefined and fixed. The size d of the permutation key is preferably made greater than the size of the intermediate current value X_{α} and the selected d bits preferably comprise the current intermediate value X_{α}.
Here the oneway function applied by the surjective permutation means 326a is therefore the result of applying d=k successive permutations of size k1=2k (i.e. e=k1=2k), each permutation being associated with a distinct bit of the permutation key C=V_{int1 }and chosen as a function at least of the value of this bit (for example in a predefined permutation table, as described below with reference to
P defines a oneway function because the permutation key C=V_{int1 }depending on the data to which the permutation function P is applied (since V_{prov}=(
In the sense of the invention the calculation means 326 therefore consist of a cryptographic module.
In the embodiment described here, the calculation means 5 of the pseudorandom generator 1 further include fourth calculation means 325c that select a section of k bits from the k1 bits of the current value of the result vector V_{res }to form the current value of a second intermediate vector V_{int2}. For example, the second intermediate vector V_{int2 }is formed by the first k bits of the result vector V_{res}.
Moreover, the calculation means 5 of the pseudorandom generator 1 here further include fifth calculation means 327 including an exclusiveOR gate 327a combining the preceding value V_{n1 }of the state vector and the current value of the second intermediate state vector V_{int2}. In addition to being nonreversible, this exclusiveOR operation confers a greater spread on the pseudorandom generator 1.
In another embodiment of the invention, the exclusiveOR gate 327a of the fifth calculation means 327 combines the current value of the second intermediate state vector V_{int2 }with the current value of the first intermediate state vector V_{int1}.
In a further embodiment of the invention, the current value V_{n }of the state vector V corresponds to the current value of the second intermediate state vector V_{int2}.
After the above operations of iteration n, the current value V_{n }of the state vector V is available for the next iteration n+1.
In the example represented in
Encryption Method and Device
The state vector V comprises a predetermined number k of bits and the initial value V_{0 }of the state vector corresponds to a configurable encryption/decryption key of size k. The size k of the encryption/decryption key corresponds to the number of bits of the key and thus to the number of bits of the state vector V.
Moreover, an input or output word U_{n}/Y_{n }is of a size m corresponding to the number of bits that are encrypted or decrypted by the encryption/decryption module 17 on each iteration. These values k and m can be predefined.
Embodiments in which the size of an input or output word can be variable are described in detail below with reference to
In the example envisaged here, the generation means 11 include a pseudorandom generator 1 of the invention as shown in
Accordingly, on each iteration n, the pseudorandom generator 1 calculates a current value V_{n }of the state vector by a noninvertible application depending on the preceding value V_{n1 }of the state vector and the current intermediate value X_{α} produced by a calculation carried out by the encryption/decryption module 17 and depending on the preceding value V_{n1 }of the state vector and the current input word U_{n }(respectively Y_{n}), and the encryption/decryption module 17 calculates a current output word Y_{n }(respectively U_{n}) by a reversible application depending on a current input word U_{n }(respectively Y_{n}) and the preceding value V_{n1 }of the state vector.
Note that the encryption device 7 can be used reversibly for encryption and/or decryption. As described above, the encryption method of the invention can be used in encryption mode when the sequence of input words is from a message in clear to be encrypted or in decryption mode when the sequence of output words is from an encrypted message to be decrypted.
In the present example, on each iteration n the pseudorandom generator 1 feeds the state vector with the current intermediate value X_{α }produced by a calculation carried out by the encryption/decryption module 17 and depending on the preceding value V_{n1 }of the state vector and the current input word U_{n }(respectively Y_{n}).
As described above, the pseudorandom generator 1 uses a noninvertible application based on a oneway function with parameters set by a permutation key and can be used to perform encryption and decryption in the same way. Moreover, the encryption/decryption module 17 is reversible and can therefore be used with the encryption/decryption operations effected in reverse order. Thus, during encryption, an input word is written U_{n }(data in clear) and an output word is written Y_{n }(encrypted data), while during decryption an input word is written Y_{n }(encrypted data) and an output word is written U_{n }(data in clear).
More specifically, before starting encryption by the encryption method of the invention, the value of the encryption key becomes the initial value V_{0 }of the state vector V (V_{0}=encryption key).
On the first iteration, the encryption/decryption module 17 calculates the first output word Y_{1 }(corresponding to an encrypted word) as a function of the first input word U_{1 }(corresponding to a word in clear) and the initial value V_{0 }of the state vector. Moreover, the pseudorandom generator 1 calculates a first vector V_{1 }of the state vector V as a function of the first input word U_{1 }and the initial value V_{0 }of the state vector. By extension, on the n^{th }iteration, the encryption/decryption module 17 calculates the current output word Y_{n }as a function of the current input word U_{n }and the preceding value V_{n1 }of the state vector. Moreover, the pseudorandom generator 1 calculates a current value V_{n }of the state vector V as a function of the current input word U_{n }and the preceding value V_{n1 }of the state vector.
In the same manner, before starting decryption by the encryption method of the invention, the value of the decryption key becomes the initial value V_{0 }of the state vector V (V_{0}=decryption key). The decryption key is naturally taken as equal to the encryption key used to encrypt the data (symmetrical encryption).
On the first iteration of the decryption process, the encryption/decryption module 17 calculates the first output word U_{1 }(corresponding to a decrypted word) as a function of the first input word Y_{1 }(corresponding to a encrypted word) and the initial value V_{0 }of the state vector. Moreover, the pseudorandom generator 1 calculates a first value V_{1 }of the state vector V as a function of the first input word Y_{1 }and the initial value V_{0 }of the state vector. By extension, on the n^{th }iteration the encryption/decryption module 17 calculates the current output word U_{n }as a function of the current input word Y_{n }and the preceding value V_{n1 }of the state vector. Moreover, the pseudorandom generator 1 calculates a current value V_{n }of the state vector V as a function of the current input word Y_{n }and the preceding value V_{n1 }of the state vector.
In the example described here, the state vector V advantageously includes a set of sections comprising at least a first state variable X, a second state variable A, a third state variable B, and possibly other state variables. These state variables are therefore pseudorandom variables. For example, the current value V_{n }of the state vector V can be structured in the following manner:
V_{n}=( . . . (X_{n}=(x_{n1 }. . . x_{nm})) . . . (A_{n}=(a_{n1 }. . . a_{nm})) . . . (B_{n}=(b_{n1 }. . . b_{nm})) . . . )
The values of the state variables X, A, and B will also be considered as sections of the state value or of the value of the state vector in the sense of the invention.
In this example, the state variables X, A, and B are sections each consisting of m consecutive bits. The current value X_{n }of the first state variable X comprises m bits X_{n1}, . . . , X_{nm}, the current value A_{n }of the second state variable A comprises m bits A_{n1}, . . . , A_{nm}, and the current value B_{n }of the third state variable B comprises m bits B_{n1}, . . . , B_{nm}.
More specifically, the value X_{n }of the first state variable X is used in the next iteration by functions (respectively means) referred to as “isolation” functions (respectively means) of the encryption/decryption module 17 before being replaced by the intermediate value X_{α} produced by the calculation effected in the next iteration by the encryption/decryption module 17. The values A_{n }and B_{n }of the second and third state variables are also used during the next iteration by the isolation functions of the encryption/decryption module 17 (see for example
The state variables are preferably located at a fixed position, but it is possible to assign them a position variable as a function of the value or values taken by one or more sections of the state vector, themselves at fixed positions. Only the solution of a fixed position of the state variables is described below.
Moreover, it is preferable (although not necessary) for the sectors assigned to each of the state variables not to overlap. The size k of the state vector is therefore chosen accordingly and each state variable corresponds to a section of limited size of the state vector (i.e. of a size strictly less than that of the state vector).
In this first example, the pseudorandom generator 1 includes transmission means 21, reception means 23, and calculation means 25, 26, and possibly 27.
On each iteration (for example on iteration n), the transmission means 21 send the encryption/decryption module 17 the preceding value V_{n1 }of the state vector comprising at least the preceding value X_{n1 }of the first state variable X, the preceding value A_{n1 }of the second state variable A, and the preceding value B_{n1 }of the third state variable B.
The reception means 23 receive from the encryption/decryption module 17 the current intermediate value X_{α}.
First calculation means 25 replace the preceding value X_{n1 }of the first state variable X by the current intermediate value X_{α }to calculate a current value of a first intermediate state vector V_{int1}.
Second calculation means 26 comprise surjective permutation means 26a adapted to apply to the first intermediate state vector V_{int1 }a oneway function with parameters set by a permutation key C of size d=k comprising the current value of the first intermediate vector V_{int1 }(C=V_{int1}) to form the second intermediate state vector V_{int2}. The second calculation means 26 function in a similar way (apart from the size of the vectors) to the calculation means 326 described above and constitute a cryptographic module in the sense of the invention.
The oneway function applied by the calculation means 26a is based on the configurable permutation function P described above (p=d=k and e=k) and therefore is here the result of applying k successive permutations of size k, each permutation being associated with a distinct bit of the permutation key C=V_{int1 }and chosen as a function at least of the value of that bit.
Accordingly, the means 26a apply the oneway function P=(V_{int1}, V_{int1}) with parameters set by the current value of the first intermediate state vector V_{int1 }to the first intermediate state vector to form a current value of a second intermediate state vector V_{int2}. In this first example, in the sense of the invention, the first intermediate value, respectively the second intermediate value, therefore represents a provisional vector, respectively a result vector. Note that the vectors V_{int1 }and V_{int2 }are both of size k. The current value V_{n }of the state vector V therefore corresponds to the current value of the second intermediate state vector V_{int2}.
In another variant (represented in dashed line in
In another variant (not shown), the third calculation means 27 include an exclusiveOR gate 27a combining the preceding value of the state vector V_{n1 }and the current value of the second intermediate state vector V_{int2}.
Thus the calculation means 5 of the pseudorandom generator 1 execute a oneway, (i.e. noninvertible) function on the first intermediate state vector V_{int1 }the result of which is optionally combined with this first intermediate state vector V_{int1 }or with the state vector in the preceding iteration.
After the above operations of iteration n, the current value V_{n }of the state vector V is available for the next iteration n+1.
Moreover, the encryption/decryption module 17 includes reception means 33, isolation means 35a and 35b and, in the example described here, connection means 37 between the isolation means 35a and 35b.
The reception means 33 receive from the pseudorandom generator 1 the preceding value V_{n1 }of the state vector comprising at least the preceding value X_{n1 }of the first state variable X, the preceding value A_{n1 }of the second state variable A, and the preceding value B_{n1 }of the third state variable B.
The isolation means comprise at least two isolation means 35a and 35b for isolating the current intermediate value X_{α}.
The isolation means apply a symmetrical “secret key” function, the secret key being obtained from at least one section of the preceding value of the state vector. As the person skilled in the art knows, a symmetrical secret key function is one for which calculating the output as a function of the input and the input as a function of the output is easy if the secret key is available and impossible if the secret key is not known.
The secret key functions used preferably include at least one exclusiveOR operation, i.e. the isolation means include at least one exclusiveOR gate. They can further include bijective permutation means.
In the example described here (see
Thus the encryption device 7 includes two interconnected elements, namely a pseudorandom generator 1 with parameters set by an encryption/decryption key of any size k used to initialize the state vector V and an encryptiondecryption module 17 incorporating secret key isolation functions.
More specifically,
The first isolation means 35a include first and second bijective permutation means 39a, 39b separated by a first exclusiveOR gate 41a. The second isolation means 35b include third and fourth bijective permutation means 39c, 39d separated by a second exclusiveOR gate 41c.
The bijective permutation means 39a, 39b, 39c, 39d considered here each implement the permutation function P described above with parameters set by a state variable of the state vector V_{n1}, i.e. by a permutation key of size m (p=m) equal to a state variable of the state vector V_{n1}. Accordingly:

 the first bijective permutation means 39a implement a first bijective permutation corresponding to the permutation function P with parameters set by a permutation key equal to the preceding value of the second state variable A_{n1};
 the second bijective permutation means 39b implement a second bijective permutation corresponding to the permutation function P with parameters set by a permutation key equal to the preceding value of the first state variable X_{n1};
 the third bijective permutation means 39c implement a third bijective permutation corresponding to the permutation function P with parameters set by a permutation key equal to the preceding value of the first state variable X_{n1}; and
 the fourth bijective permutation means 39d implement a fourth bijective permutation corresponding to the permutation function P with parameters set by a permutation key equal to the preceding value of the third state variable B_{n1}.
The permutation keys used to set the parameters of the permutation function P in the bijective permutation means 39a, 39b, 39c, and 39d being independent of the data to which the resulting permutation function P is applied, each therefore implements an invertible (bijective) function the invert function of which is a permutation function P^{−1}. This invertible function P is the result of applying m successive permutations of size m (p=e=m) selected as a function of the value of each bit of the permutation key concerned.
Thus, in this encryption mode, calculating a current output word Y_{n }during an iteration n includes the following operations.
The first permutation means 39a calculate a first intermediate word G_{1n }by applying the first bijective permutation to a pair consisting of the current input word U_{n }and a preceding value A_{n1 }of the second state variable: G_{1n}=P(U_{n}, A_{n1}). In other words, the first permutation means 39a calculate the first intermediate word G_{1n }by applying to the current input word U_{n }the bijective permutation function P with parameters set by A_{n1}.
The first exclusiveOR gate 41a calculates a second intermediate word G_{2n }by applying an exclusiveOR operation to the first intermediate word G_{1n }and the preceding value A_{n1 }of the second state variable: G_{2n}=G_{1n}⊕A_{n1}.
The second permutation means 39b calculate a third intermediate word G_{3n }by applying the second bijective permutation to a pair consisting of the second intermediate word G_{2n }and the preceding value X_{n1 }of the first state variable: G_{2n}=P(G_{2n},X_{n1}). In other words, the second calculation means 39b calculate the third intermediate word G_{3n }by applying the bijective permutation function P with parameters set by X_{n1 }to the second intermediate word G_{2n}.
The central exclusiveOR gate 41b calculates the current intermediate value X_{α }by applying an exclusiveOR operation to the third intermediate word G_{3n }and the preceding value X_{n1 }of the first state variable: X_{α}=G_{3n}⊕X_{n1}. This current intermediate value X_{α }is then sent to the pseudorandom generator 1.
The third permutation means 39c then calculate a fourth intermediate word G_{4n }by applying the third bijective permutation to a pair consisting of the current intermediate value X_{α }and the preceding value X_{n1 }of the first state variable: G_{4n}=P(X_{α}, X_{n1}). In other words, the third permutation means 39c calculate the fourth intermediate word G_{4n }by applying the bijective permutation function P with parameters set by X_{n1 }to the current intermediate value X_{α}.
The third exclusiveOR gate 41c calculates a fifth intermediate word G_{5n }by applying an exclusiveOR operation to the fourth intermediate word G_{4n }and the preceding value B_{n1 }of the third state variable: G_{5n}=G_{4n}αB_{n1}.
Finally, the fourth permutation means 39d calculate the current output word Y_{n }by applying the fourth bijective permutation to a pair formed by the fifth intermediate word G_{5n }and a preceding value B_{n1 }of the third state variable: Y_{n}=P(G_{5n}, B_{n1}). In other words, the fourth permutation means 39d calculate the current output word Y_{n }by applying the bijective permutation function P with parameters set by B_{n1 }to the fifth intermediate word G_{5n}.
In this decryption mode the calculation of a current output word U_{n }in an iteration n includes the following operations.
The fourth permutation means 39d calculate a fifth intermediate word G_{5n }by applying a permutation that is the reverse of the fourth bijective permutation to a pair formed by a current input word Y_{n }and the preceding value B_{n1 }of the third state variable: G_{5n}=P^{−1}(Y_{n}, B_{n1}).
The third exclusiveOR gate 41c calculates a fourth intermediate word G_{4n }by applying an exclusiveOR operation to the fifth intermediate word G_{5n }and the preceding value B_{n1 }of the third state variable: G_{4n}=G_{5n}⊕B_{n1}.
The third permutation means 39c calculate the current value X_{α} by applying a permutation that is the reverse of the third bijective permutation to a pair formed by the fourth intermediate word G_{4n }and the preceding value X_{n1 }of the first state variable: X_{α}=P^{−1}(G_{4n}, X_{n1}). This current intermediate value X_{α} is then sent to the pseudorandom generator.
The center exclusiveOR gate 41b calculates a third intermediate word G_{3n }by applying an exclusiveOR operation to the current intermediate value X_{α} and the preceding value X_{n1 }of the first state variable: G_{3n}=X_{α}⊕X_{n1}.
The second permutation means 39b calculate a second intermediate word G_{2n }by applying a permutation that is the reverse of the second bijective permutation to a pair formed by the third intermediate word G_{3n }and the preceding value X_{n1 }of the first state variable: G_{2n}=P^{−1}(G_{3n}, X_{n1}).
The first exclusiveOR gate 41a calculates a first intermediate word G_{1n }by applying an exclusiveOR operation to the second intermediate word G_{2n }and the preceding value A_{n1 }of the second state variable: G_{1n}=G_{2n}⊕A_{n1}.
Finally, the first permutation means 39a calculate the current output word U_{n }by applying a permutation that is the reverse of the first bijective permutation to a pair formed by the first intermediate word G_{1n }and the preceding value A_{n1 }of the second state variable: U_{n}=P^{−1}(G_{1n}, A_{n1}).
Accordingly, in the
Moreover, in one embodiment, the complexity of the encryption/decryption operations can be further increased by replacing each of the state variables A_{n}, B_{n}, and X_{n }by two subvariables of identical size (sections in the sense of the invention), respectively A_{n}′ and A_{n}″ for A_{n}, B_{n}′, and B_{n}″ for B_{n }and X_{n}′, and X_{n}″ for X_{n}. The subvariables A_{n}, B_{n}′, and X_{n}′ can be used to set the parameters of the permutations P and P^{−1 }and the subvariables A_{n}″, B_{n}″, and X_{n}″ can be used to calculate the exclusiveOR operations.
In another embodiment, the respective state subvariables A_{n}′ and A_{n}″ for A_{n}, B_{n}′, and B_{n}″ for B_{n }and X_{n}′, and X_{n}″ for X_{n }can be noncontiguous and each of size m. For example:
V_{n}=(X′_{n}A′_{n}B′_{n}X″_{n}A″_{n}B″_{n }. . . )
In a further embodiment, each state variable can include m not necessarily consecutive bits of the state vector V occupying predetermined positions, for example.
Use of a Plurality of PseudoRandom Generators in Parallel
Moreover, note that in one particular embodiment of the invention it is possible to use a plurality of generators in parallel for the same encryption/decryption module.
For example,
The first pseudorandom generator 101 forms a first current value V1_{n }of a first state vector V1 and the second pseudorandom generator 102 forms a second current value V2_{n }of a second state vector V2.
The two pseudorandom generators 101, 102 can be combined in parallel by means of an exclusiveOR gate, for example. The current value V_{n }of the state vector is then the result of an exclusiveOR operation applied to the first current value V1_{n }of the first state vector and the second current value V2_{n }of the second state vector. Note that any other combination is possible, for example the current value V_{n }of the state vector coming from the two pseudorandom generators 101, 102 can be made up of a first section derived from the first current value V1_{n }of the first state vector, a second section derived from the second current value V2_{n }of the second state vector, and a third section derived from any combination of the corresponding sections of the first and second current values V1_{n}, V2_{n }of the first and second state vectors.
More specifically, in the
In this specific example, the preceding value V_{n1 }of the state vector sent to the encryption/decryption module 17 is formed by a preceding value X_{n1 }of the first state variable X resulting from an exclusiveOR operation applied to the first preceding value X1_{n1 }of the first state variable X1 of the first state vector and the second preceding value X2_{n1 }of the first state variable X2 of the second state vector, a preceding value A_{n1}=A1_{n1 }of the second state variable A1 of the first state vector and a preceding value B_{n1}=B2_{n1 }of the third state variable B2 of the second state vector. Moreover, the two pseudorandom generators 101, 102 are fed the same current intermediate value X_{α} from the encryption/decryption module 107.
Thus, generally speaking, it is possible to implement h pseudorandom generators in parallel (i=1 to h) for the same encryption/decryption module. The h pseudorandom generators are then all fed the same current intermediate value X_{α }from the encryption/decryption module. The h generators can be of the same or different sizes k_{1}, . . . , k_{h}. The initial values V1_{0}, . . . , Vh_{0 }can be extracted or calculated from the same common encryption/decryption key, the size of which is equal to the maximum of k_{1}, . . . , k_{h}. The values of A_{n }and B_{n }can come from the same generator or different generators. X_{n }can correspond to the result of combining by means of exclusiveOR operations all of the respective Xi_{n}: X_{n}=X1_{n}⊕X2_{n}⊕ . . . ⊕Xh_{n}.
Of course, the pseudorandom generators in parallel can be used independently of the encryption/decryption module to generate a pseudorandom data sequence of high quality.
Varying the Number of Bits of the Input and Output Words.
In the above examples, the state vector comprises a particular number k of bits and each output or input word comprises a particular number m of bits less than the particular number k of bits of the state vector.
In one particular embodiment of the invention, each output or input word can advantageously comprise a number w of bits that can vary on each iteration whilst remaining less than the particular number k of bits of the state vector.
Here the state vector V can advantageously include a fourth state variable E indicating this number w of bits that is variable on each iteration to adapt the permutations (in particular the size e of the permutations and the number p of stages of permutation concerned) and exclusiveOR operators implemented by the permutation means and the exclusiveOR gates of the module 17 for encrypting/decrypting to this variable number w.
Accordingly, the permutation functions P (for encryption), P^{−1 }(for decryption) and the exclusiveOR operator “⊕” used by the encryption/decryption module 17 are adaptable to input and output words U_{n}/Y_{n }of any length w (w≦m<k). Provided that permutation tables are predefined corresponding to all feasible values of w to implement the permutation functions P and P^{−1 }to effect the exclusiveOR operations on the first w bits of the state variables A_{n1}, X_{n1}, and B_{n1}, it is possible to divide the input data into blocks of variable size w and to encrypt and/or decrypt those blocks using the encryption/decryption module 17.
The parameter indicating the number w of input bits to be encrypted and/or decrypted during iteration n is provided by the preceding value E_{n1 }of the fourth state variable E. This fourth state variable E is a section of size r of the state vector isolated from the inputs and outputs and depending on the encryption/decryption key and the whole of the applied sequence of input words U_{n}/Y_{n}.
Accordingly, during iteration n, the size w_{n1 }of the block to be processed is sent to the input word U_{n}/Y_{n }or the output word Y_{n}/U_{n }and to the permutation means 39a39d and to the logic gates 41a41c to size the permutations and the exclusiveOR operations.
The number of bits encrypted on each iteration is therefore pseudorandom, depending on the encryption/decryption key and the whole of the applied sequence of input words U_{n}/Y_{n}. The slightest modification of the input word sequence U_{n}/Y_{n }therefore systematically leads to modification of the whole of the subdivision of the data after that modification.
To extract the number w of bits to encrypt/decrypt during the iteration n from the preceding value E_{n1 }of the fourth state variable E, w can be assigned the decimal value coded on the r bits of the preceding value E_{n1 }of the fourth state variable: 0≦w≦2^{r}−1 (=m). Alternatively, w can be assigned the value of the number of bits at 1 in the preceding value E_{n1 }of the fourth state variable: 0≦w≦r (=m).
Note that in the example described here the initial number of bits is set to w_{0}=1 by convention and regardless of the initial value E_{0 }of the fourth state variable E. Thus only one bit is systematically encrypted/decrypted during the first iteration.
To prevent leaking of information concerning the subdivision effected (for example by observing the inputs and outputs of the encryption module) the output words Y_{n}/U_{n }can advantageously be grouped to free up at the output blocks of constant length m only. The same precaution can be applied to the input words U_{n}/Y_{n }in the case of decryption.
Thus the pseudorandom generator 1 includes fourth calculation means 45 including additional surjective permutation means. Thus the pseudorandom generation step of each iteration includes application by the fourth calculation means 45, when the variable number w is equal to zero, of a surjective permutation to the current value V_{n }of the state vector (permutation function P with parameters set by a permutation key equal to the vector V_{n}) to form a current value of an additional second intermediate state vector V2_{ins}. This current value of the second additional intermediate state vector V2_{ins }then replaces the current value V_{n }of the state vector V.
Alternatively, the pseudorandom generator 1 can include fifth calculation means 47 including an additional exclusiveOR gate 47a for calculating a new current value V_{temp }of the state vector by applying an exclusiveOR operation to the current value of the additional second intermediate state vector V2_{ins }and the current value V_{n }of the state vector. This new current value V_{temp }of the state vector then replaces the current value V_{n }of the state vector.
Thus
More specifically, before starting an encryption process, the value of the encryption key becomes the initial value V_{0 }of the state vector V: V_{0}=encryption key and w_{0}=1.
On the first iteration, the encryption/decryption module 17 takes the first bit of the input word U_{1 }to be encrypted and calculates the value of the first bit of the output word Y_{1 }encrypted as a function of U_{1 }and the initial value V_{0 }of the state vector V. The pseudorandom generator 1 calculates a first value V_{1 }of the state vector V as a function of U_{1 }and V_{0}.
By extension, on the n^{th }iteration, if the pseudorandom generator 1 detects that w_{n1}=0, the pseudorandom generator 1 effects “empty” iterations on the preceding value V_{n1 }of the state vector for as long as w_{n1}=0.
In contrast, if w_{n1}≠0, the encryption/decryption module 17 takes the next w_{n1 }bits of the data to be encrypted (block U_{n}) and calculates the value of the output word Y_{n }as a function of U_{n }and V_{n1}. The pseudorandom generator 1 calculates a new value V_{n }of the state vector V as a function of U_{n }and V_{n1}.
Symmetrically, before decryption, the value of the decryption key becomes the initial value V_{0 }of the state vector V: V_{0}=decryption key and w_{0}=1.
On the first iteration, the encryption/decryption module 17 takes the first bit of the input word Y1 to be decrypted and calculates the value of the first bit of the output word U1 decrypted as a function of Y1 and the initial value V0 of the state vector V. The pseudorandom generator 1 calculates a first value V1 of the state vector V as a function of Y1 and V0.
By extension, on the n^{th }iteration, if the pseudorandom generator 1 detects that w_{n1}=0, the pseudorandom generator 1 effects “empty” iterations on the preceding value V_{n1 }of the state vector for as long as w_{n1}=0.
In contrast, if w_{n1}≠0, the encryption/decryption module 17 takes the next w_{n1 }bits of the data to be decrypted (block Y_{n}) and calculates the value of the output word U_{n }as a function of Y_{n }and V_{n1}. Furthermore, the pseudorandom generator 1 calculates a new value V_{n }of the state vector V as a function of Y_{n }and V_{n1}.
Accordingly, the operations of the
Note moreover that in order to avoid desynchronization of streams and empty cycles the size of the blocks to be encrypted/decrypted can be varied without having to address the situation where w=0; in this situation where w=0 only one bit must be encrypted/decrypted.
It is also possible to retain only the stream desynchronization function without varying the size of the blocks to be encrypted/decrypted. An empty cycle of the pseudorandom generator 1 is then effected if w=0 whereas for any other value of w an input word U_{n}/Y_{n }or an output word Y_{n}/U_{n }of fixed size m is encrypted/decrypted.
Cryptographic Multiplexing
The various embodiments of the encryption method and device of the invention can be used for high bit rate stream encryption applications (telecommunications, protected multimedia content broadcasting, on the fly encryption of data in servers, personal computers and software applications, etc.). Furthermore, the very structure of the encryption process suits it to applications in the field of cryptographic multiplexing.
Generally speaking, cryptographic multiplexing causes M messages in clear 71 to be encrypted to converge toward the same encryption device 207a, which generates M encrypted messages. These M encrypted messages are then combined and sent via the same channel 73a (
An encryption device 207b used in decryption mode (also referred to as a decryption device) then reconstitutes the M messages 75 in clear from the M encrypted messages. It is impossible to reconstitute only one of the M messages in clear if the M encrypted messages are not available or all of them. This solution pools the cryptographic application and offers a simple and effective solution for protecting multiple contents that have to be routed over one or more nonsecured channels.
The encryption method of the invention effects cryptographic multiplexing as described above using only one pseudorandom generator sized accordingly and M encryption/decryption modules in parallel. This enables an extremely simple hardware or software implementation benefiting from the performance of the encryption method in terms of speed and cryptanalysis resistance, as well as variable size block, empty iteration and stream desynchronization functions applied to M different messages.
In this situation, the pseudorandom generator 1 calculates on each iteration a current value of a state vector including a first set of state variable sections and at least one second set of state variable sections.
Generally speaking, to multiplex M messages (M=2 in
V_{n}=( . . . X1_{n},A1_{n},B1_{n},E1_{n}, . . . X2_{n},A2_{n},B2_{n},E2_{n}, . . . XM_{n},AM_{n},BM_{n},EM_{n}, . . . )
Moreover, the first encryption/decryption module 17a calculates a first current output word Y1_{n}/U1_{n}, by a first reversible application depending on a first current input word U1_{n}/Y1_{n }and the first set of sections X1_{n1}, A1_{n1}, B1_{n1}, E1_{n1 }of the preceding value V_{n1 }of the state vector. The intermediate value X1_{α }is sent to the pseudorandom generator 1.
The second encryption/decryption module 17b calculates a second current output word Y2_{n}/U2_{n }by a second reversible application depending on a current input word U2_{n}/Y2_{n }and the second set of sections X2_{n1}, A2_{n1}, B2_{n1}, E2_{n1 }of the preceding value V_{n1 }of the state vector. The intermediate value X2_{α }is sent to the pseudorandom generator 1.
In this example, the cryptographic multiplexing means 81 can multiplex at least two message blocks in clear to form at least two encrypted message blocks, each message block in clear corresponding to a succession of input words. The cryptographic multiplexing means 81 correspond to the setting the parameters of a pseudorandom generator 1 as shown in the above figures by a state vector including a fifth state variable F. Accordingly, the pseudorandom generator 1 can order the various message blocks encrypted on each iteration as a function of the fifth state variable F in the state vector.
Consequently, the order in the transmission channels of the M blocks encrypted on each iteration, whether combined or not, can be predefined or a function of a nonaccessible pseudorandom variable (a section of the state vector), depending on the encryption key in encryption mode (respectively the decryption key in decryption mode) and the whole of the applied sequence of input words. For example, the M encrypted blocks, whether combined or not, can be ordered by the permutation function P with parameters set by the fifth state variable F included in the state vector.
The parameter for ordering the M blocks of the encrypted message combined during iteration n is supplied by the preceding value F_{n1 }of the fifth state variable F, F_{n1 }being a section of size M of the preceding value V_{n1 }of the state vector, isolated from the input words and the output words and depending on the encryption key (respectively the decryption key) and the whole of the sequence of input words applied.
The order in the transmission channels of the M blocks of the encrypted message on each iteration, combined or not, is therefore pseudorandom, depending on the encryption key (respectively the decryption key) and the whole of the applied sequence of input words. The slightest modification to the sequence of input words therefore leads systematically to complete modification of the order of the blocks of the encrypted message in the transmission channels, combined or not, after that modification.
Cryptographic Hashing Method and Device
Note that
In the embodiment described in detail here, the state vector V includes a predetermined number k of bits and the initial value V_{0 }of the state vector corresponds to a configurable hashing key of size k.
This device 407 includes means for dividing the message Mess into a predetermined number M of blocks Z_{1}, Z_{2}, . . . , Z_{M }of predetermined size (for example M blocks each of m bits). In a manner that is known in the art, if the last block in the subdivision is incomplete (i.e. does not comprise m bits), the incomplete block is padded out with bits at 0.
The device 407 further includes generation means for iteratively generating a succession 13 of M values of a state vector V from an initial value V_{0 }of the state vector and obtaining a digest hash of the message Mess from the latest value V_{M }of the state vector generated. The message blocks Z_{1}, Z_{2}, . . . , Z_{M }are used in turn by the generation means during successive iterations to generate the M values of the state vector.
In the example envisaged here, the generation means include a pseudorandom generator 1 of the invention (for example the pseudorandom generator shown in
On each iteration n, the pseudorandom generator 1 calculates a current value V_{n }of the state vector using a noninvertible application depending on the preceding value V_{n1 }of the state vector and an intermediate current value X_{α} produced by a calculation carried out by the preconditioning module 417, the preconditioning module 417 calculating the current intermediate value X_{α }using an invertible application depending on the preceding value V_{n1 }of the state vector and a current message block Z_{n }(input block in the sense of the invention). On each iteration n the pseudorandom generator 1 feeds the state vector V_{n }with the current intermediate value X_{α }from the preconditioning module 417.
On the first iteration, the preconditioning module 417 calculates the current intermediate value X_{α }for iteration 1 as a function of the first message block Z_{1 }and the initial value V_{0 }of the state vector. The pseudorandom generator 1 calculates a first value V_{1 }of the state vector V as a function of the first message block Z_{1 }and the initial value V_{0 }of the state vector. By extension, on the n^{th }iteration, the preconditioning module 417 calculates the current intermediate value X_{α }for iteration n as a function of the current message block Z_{n }and the preceding value V_{n1 }of the state vector and the pseudorandom generator 1 calculates a current value V_{n }of the state vector V as a function of the current message block Z_{n }(using the current intermediate value X_{α}) and the preceding value V_{n1 }of the state vector.
In the embodiment described here, the state vector V advantageously includes a set of sections including at least one first state variable X and one second state variable A of size m. For example, the current value V_{n }of the state vector V can be structured in the following manner where, in the sense of the invention, the state variables X and A are sections of the state vector:
V_{n}=( . . . (X_{n}=(x_{n1 }. . . x_{nm})) . . . (A_{n}=(a_{n1 }. . . a_{nm})) . . . )
In this example, the current value X_{n }of the first state variable X comprises m bits X_{n1}, . . . , X_{nm }and the current value A_{n }of the second state variable A comprises m bits a_{n1}, . . . , a_{nm}, where m is the size of the message blocks Z_{n}, n=1, . . . , M.
The locations of the state variables are predefined and preferably fixed, but it is possible to assign them a position variable as a function of the value or values taken by one or more sections of the state vector, themselves of fixed position. Only the solution of a fixed position of the state variables is described below.
Moreover, it is preferable (although not necessary) for the sectors assigned to each of the state variables not to overlap. The size k of the state vector is then chosen accordingly, and each state variable corresponds to a section of the state vector of limited size (i.e. of size strictly less than that of the state vector).
Of course, the variants of the state variables described above in the context of an encryption method are equally applicable in the context of a cryptographic hashing method of the invention.
The value X_{n }of the first state variable X is used in a subsequent iteration by an isolation function of the preconditioning module 417 before it is replaced by the intermediate value X_{α} produced by the calculation carried out in the next iteration by the preconditioning module 417. The value A_{n }of the second state variable is also used in the next iteration by the isolation function of the preconditioning module 417.
On each iteration (for example on iteration n), the transmission means 321 of the pseudorandom generator 1 send the preconditioning module 417 the preceding value V_{n1 }of the state vector including at least the preceding value X_{n1 }of the first state variable X and the preceding value A_{n1 }of the second state variable A.
The reception means 323 of the pseudorandom generator 1 receive from the preconditioning module 417 the current intermediate value X_{α}.
The first calculation means 325a replace the preceding value X_{n1 }of the first state variable X by the current intermediate value X_{α} to calculate a current value of a first intermediate state vector V_{int1}. The other process steps and means of the pseudorandom generator 1 are similar to those described with reference to
The preconditioning module 417 includes reception means 433 and isolation means 435 for isolating the current intermediate value X_{α} from the message blocks.
The reception means 433 receive from the pseudorandom generator 1 the preceding value V_{n1 }of the state vector including at least the preceding value X_{n1 }of the first state variable X and the preceding value A_{n1 }of the second state variable A.
The isolation means 435 are adapted to apply a symmetrical secret key function to each message block Z_{n}, the secret key being obtained from at least one section of the preceding value of the state vector.
The secret key function used preferably includes at least one exclusiveOR operation, i.e. the isolation means 435 include at least one exclusiveOR gate with parameters set by a section of size m of the preceding value of the state vector. Alternatively, it can further include at least one bijective permutation in the sense of the invention with parameters set by a section of size m of the preceding value of the state vector.
In the example described here, the secret key function used by the isolation means 435 is made up of two bijective permutations in the sense of the invention and two exclusiveOR operations each with parameters set by a section of size m of the state vector V_{n1}. The secret key of this function is made up of the section setting the parameters of the first bijective permutation, the section setting the parameters of the first exclusiveOR operation, the section setting the parameters of the second bijective permutation, and the section setting the parameters of the second exclusiveOR operation.
Thus the isolation means 435 include first and second bijective permutation means 439a and 439b separated by a first exclusiveOR gate 441a. A second exclusiveOR gate 441b receives the output of the second bijective permutation means 439b.
The bijective permutation means 439a and 439b considered here each use the permutation function P described above, with parameters set by respective different state variables of the state vector V_{n1}. In other words, the abovementioned different bijective permutation means use a permutation key of size m equal to a state variable of the state vector V_{n1}. Accordingly:

 the first bijective permutation means 439a use a first bijective permutation corresponding to the permutation function P with parameters set by a permutation key equal to the preceding value of the second state variable A_{n1}; and
 the second bijective permutation means 439b use a second bijective permutation corresponding to the permutation function P with parameters set by a permutation key equal to the preceding value of the first state variable X_{n1}.
The permutation keys used to set the parameters of the permutation function P in the bijective permutation means 439a and 439b are independent of the data to which the resulting permutation function P is applied, and each therefore uses an invertible (bijective) function. This invertible function P is the result of applying m successive permutations of size m selected as a function of the value of each bit of the permutation key concerned.
Thus calculating the current intermediate value X_{α} in an iteration n includes the following operations:

 the first permutation means 439a calculate a first intermediate word J_{1n }by applying the first bijective permutation to the current input block Z_{n}, that permutation having parameters set by a preceding value A_{n1 }of the second state variable: J_{1n}=P(Z_{n}, A_{n1});
 the first exclusiveOR gate 441a calculates a second intermediate word J_{2n }by applying an exclusiveOR operation to the first intermediate word J_{1n }and the preceding value A_{n1 }of the second state variable: J_{2n}=J_{1n}⊕A_{n1};
 the second permutation means 439b calculate a third intermediate word J_{3n }by applying the second bijective permutation to the second intermediate word J_{2n}, that permutation having parameters set by a preceding value X_{n1 }of the first state variable: J_{3n}=P(J_{2n}, X_{n1});
 the second exclusiveOR gate 441b calculates the current intermediate value X_{α }by applying an exclusiveOR operation to the third intermediate word J_{3n }and the preceding value X_{n1 }of the first state variable: X_{α}=J_{3n}⊕X_{n1}.
This current intermediate value X_{α }is then sent to the pseudorandom generator 1.
Note that modifying one bit of the current block Z_{n }(i.e. the message block in the process of being hashed) modifies a bit of the variable X_{α} incorporated in the state vector V_{n1 }by the calculation means 325a of the pseudorandom generator 1 to form the first intermediate vector V_{int1 }in iteration n. Consequently, the choice of the permutations implemented by the calculation means 326 is assigned to one stage of permutation, and thus in consequence the whole of the state vector V_{n }and the subsequent state vectors will also be modified (avalanche effect).
After M successive iterations using the M message blocks constituting the message Mess, the digest hash of the message Mess is formed by the cryptographic hashing device 407 from the latest (i.e. the M^{th}) state vector generated by the pseudorandom generator 1, in other words: hash=V_{M}.
This provides for extremely simple hardware or software implementation of a cryptographic hashing method and device benefiting from the speed and cryptanalysis resistance performance of the pseudorandom generation method.
Moreover, in accordance with principles similar to those implemented for the encryption device of the invention, it is possible to consider message blocks Z_{n }of a size variable as a function of the iteration (i.e. subdividing the message Mess as the iterations proceed into blocks whose size w is variable and specified in a section of the state vector) and/or to desynchronize the operations effected in the preconditioning module and in the pseudorandom generator (in particular by introducing “empty iterations” as described for the encryption device.
Moreover, in one particular embodiment of the invention it is equally possible to chain h hashing devices sequentially (a section of a state vector generated by the pseudorandom generator of a hashing device feeding the preconditioning module of the next hashing device) to increase the mathematical complexity of the cryptographic hashing.
Moreover, in one particular embodiment of the invention, it is possible to effect the cryptographic hashing by the hashing method of the invention simultaneously with encrypting (respectively decrypting) the message using the architecture of the encryption method of the invention.
Implementation of the Permutation Function P
How the permutation function P used in the above examples works is described in more detail below with reference to
As mentioned above, in a manner that is highly advantageous here, the pseudorandom generator (and generation method), the encryption device (and method), and the cryptographic hashing device (and method) rely on the same permutation function P proposed by the invention with parameters set by a permutation key and parameters that can be set as a function of the size of the input data and the key concerned.
Thus the permutation function P in these examples has the advantage of addressing a plurality of requirements.
In one case, the size of the permutation key is equal to the size of the input data that is also equal to the size of the output data (for example for encryption or cryptographic hashing, but also for pseudorandom generation in the example shown in
In another case, the size of the permutation key is strictly less than the size of the input data that is also equal to the size of the output data (for example for pseudorandom generation in the example shown in
In a further case, the permutation function P can have parameters set so that it can be applied both to the input data of size e (e=k1≧k−size of the state vector V) and m (size of the data U/V to be encrypted/decrypted). In further cases, the permutation function P can have parameters set so that it can be applied to input data of any size e=w enabling access to functions for modifying the number of bits encrypted on each iteration.
In this example, the first bit of the input data is shifted to the 3^{rd }location (box 61c) of the output data retaining its value v(1). The second bit of the input data is shifted to the k^{th }location (box 61f) of the output data retaining its value v(2). The third bit of the input data is shifted to the 4^{th }location (box 61d) of the output data retaining its value v(3). The fourth bit of the input data is shifted to the 1^{st }location of the output data retaining its value v(4). The k^{th }bit of the input data is shifted to the 2^{nd }location (box 61b) of the output data retaining its value v(k).
According to the choice made for the key relative to the input data to which the permutation function P is applied, the permutation function P is:

 a oneway function and therefore nonreversible (noninvertible) if the permutation key is generated from input data (for example key=input data); these oneway function properties are exploited in the operations carried out by the pseudorandom generator 1 and in a cryptographic module of the invention; or
 a bijective function (bijective key permutation) that is therefore reversible provided that the value of the permutation key is known and the permutation key is independent or fixed relative to the input data; these bijective function properties can be exploited in the isolation functions or means of the encryption/decryption module 17 or the preconditioning module 417 of the cryptographic hashing device.
To apply the permutation function P with parameters set by the permutation key C of size p to the data to be permutated of size e, there are chained to the data to be permutated p permutations of size e with parameters set by the value of the p bits of the permutation key, i.e. each permutation is chosen as a function of the value of a distinct bit of the permutation key.
For each bit of the permutation key, the permutation is chosen from a pair of different permutations (P0, P1) of size e predefined for each permutation stage. For example, if the bit of the permutation key considered is equal to 0 permutation P0 is chosen and if the bit of the permutation key considered is equal to 1 permutation P1 is chosen.
The permutations of size e considered can in particular be chosen from predefined pairs of permutations (P0, P1) satisfying at least one of the following conditions:

 for each bit of the key, the permutation obtained by respectively composing P0 and P1 and the permutation obtained by respectively composing P1 and P0 are different at all points;
 there is used in each of the p stages of the permutation function (a stage corresponding to the application of a permutation), an identical pair of permutations P0 and P1 different at all points, i.e., for any t, the position of the bit t at the output for the first permutation is different from the position of the bit t at the output for the second permutation;
 there is used in each stage a pair of permutations (P0; P1) such that the permutations P0 and P1 are individually different at all points from the identity permutation, i.e. a bit at position t before application of permutation P0, respectively P1, is located at a position different from t on exit from the permutation P0, respectively the permutation P1.
Alternatively, a pair of different permutations (P0_{i}, P1_{i}) can be applied in each permutation stage i.
Thus, for data of any size e to be processed, the permutation function P proceeds in two steps:

 in a first step, a table of size (p, 2e) made up of p rows each of two permutations (P0, P1) of size e, which also serves as a routing matrix in a hardware implementation, is calculated beforehand;
 in a second step, and when using the permutation function P, each row i of this table provides two possible permutations, one or the other of those permutations being chosen as a function of the value vkey(i) of the i^{th }bit of the permutation key used.
For a given permutation key value, the permutation function P thus chains to the input data p permutations of size e respectively with parameters set by the value of each of the p bits of the permutation key.
A main advantage of the permutation function P described above is its very simple hardware implementation, which can employ only “NOT” and “AND” logic functions.
The
The AND logic gate 65 corresponds in this application to a switch (or a transistor in a hardware implementation) controlled by the value vkey of a bit of the permutation key or its complement. The switch is therefore open or closed as a function of the value vkey of the bit of the key or its complement (turned on or turned off when the switch is a transistor).
The stages are therefore chained one after the other, the output 69 of the stage h1 feeding the input 67 of the stage h.
By applying to the inputs of the first stage the respective values of each bit of the data to be permutated and to the key input of each stage the respective value of the bit of the associated key there is obtained a logic function that can be executed in only one operation over all the p stages, corresponding to p permutations of size e effected on input data of size e and with parameters set by a key of size p. If an identical pair of two different permutations is used for each of the p stages, p identical modules are used.
For software implementation, a recursive function can be used having for its parameters: the input data, the permutation key, the permutation table and the permutation stage i concerned. The permutation function P is calculated extremely quickly by calling the following “recursive function” with i=p:
The hardware and software implementations described above have the advantage that they can be used regardless of the nature of the permutation key concerned (i.e. dependent on or independent of the input data to be permutated), i.e. whether the permutation function P is a oneway function or if the permutation function P is a bijective key permutation. This has the advantage of limiting the complexity of implementing the processes and devices described above.
The present invention thus provides a pseudorandom generator with parameters set by an encryption key of any size k (used as the initial value of the state vector), effecting iterations on a state vector fed on each iteration with an intermediate result coming from an encryption/decryption module, and thus depending on the whole of the applied input sequence. The encryption/decryption module integrates selfisolation functions of the pseudorandom generator and carries out on each iteration the encryption and/or decryption of input data as a function of the values of a plurality of sections of the state vector of the pseudorandom generator.
Thus the encryption device of the invention has the following advantages in particular:
The encryption/decryption module is reversible whether implemented in hardware or software. It is therefore not necessary to have different programs/circuits for the encryption and decryption functions.
The pseudorandom generator is nonreversible.
A permutation function P is effected in a single extremely fast operation whether implemented in hardware or software, used in a noninvertible form P(data,key(data)) (i.e. the key depends on the data to be permutated) in the pseudorandom generator and in an invertible form P(data, fixed_key) (i.e. the key is fixed in relation to the data to be permutated) in the encryption/decryption module.
The pseudorandom generator has no particular period and does not follow a predefined cycle. The value of the state vector depends on the encryption/decryption key and on the whole of the applied sequence of input words, with no deterministic cycle, because of switching on each iteration from one attractor (cycle specific to a particular input sequence) to another.
The state vector pseudorandom generator proposed by the invention is such that the value of the state vector cannot be reconstructed from observation of the sequences of output words or intentionally brought to a predefined value by a sequence of input words (nonobservable and noncommandable state vector). The state vector isolates input and output words using isolation functions with parameters set by the values of certain of its own state variables (selfisolation). Apart from resistance to cryptanalysis, this property eliminates problems of modification of the initialization vector each time the encryption process is started. The encryption/decryption key that serves as an initialization vector therefore need not be modified. Additionally a message header can be used beginning with a Nonce (Number used once) of the message number type in order to avoid leaking of information concerning the fact that the messages have similar headers.
The invention offers the possibility of modifying the number of bits encrypted on each iteration as a function of a pseudorandom variable that is not accessible (a section of the state vector) and depends on the encryption/decryption key and the whole of the applied sequence of input words.
Another option is for the pseudorandom generator to effect “empty cycles” (iterations effected on the state vector without encrypting the inputs), as a function of a pseudorandom variable that is not accessible (a section of the state vector) and depends on the encryption/decryption key and the whole of the applied sequence of input words, leading to desynchronization of the pseudorandom generator and the data encryption/decryption module.
A further option is to use the encryption device as a cryptographic multiplexer, by having M messages in clear to be encrypted to converge on the same encryption module that generates M encrypted messages. It is impossible to reconstruct a single one of the M messages in clear or all of them if the M encrypted messages are not accessible. The encrypted messages can be combined with each other to reduce the number of transmission channels. The order of the encrypted blocks in the transmission channel on each iteration, combined or otherwise, can be predefined or a function of a pseudorandom variable that is not accessible (a section of the state vector) and depends on the encryption key and the whole of the applied sequence of input words.
The invention finds a highly advantageous application in that it enables simultaneous cryptographic hashing and symmetrical encryption/decryption offering a high level of security and simple and efficient implementation in hardware or in software.
Note that cryptographic hashing and symmetrical encryption are routinely used in all types of communication, such as mobile communication, the Internet, smart cards, etc.
Claims
1. A cryptographic method by a pseudorandom generator of generating a current value for a state vector of size k corresponding to a current iteration of a pseudorandom data sequence formed by a succession of values for the state vector generated iteratively from an initial value of the state vector, the method comprising:
 obtaining, with a processing device, a current intermediate value calculated from a preceding value of the state vector generated in a previous iteration;
 forming, with the processing device, a permutation key by selecting d bits from a first intermediate vector of size k, wherein d is less than or equal to k and the first intermediate vector is formed from the preceding value of the state vector in which a section has been replaced by the current intermediate value;
 determining, with the processing device, d permutations, each of size k1, as a function at least of the value of a respective associated bit of the permutation key;
 successively applying, with the processing device, each of the permutations to a provisional vector of size k1 to determine a result vector, wherein k1 is greater than or equal to k and the provisional vector includes the first intermediate vector; and
 determining, with the processing device, the current value of the state vector from at least one section of said result vector.
2. A cryptographic method according to claim 1, wherein the provisional vector further includes a vector obtained by complementing to 1 each bit of the first intermediate vector.
3. A cryptographic method according to claim 1, wherein the current value of the state vector is the result of applying an exclusiveOR operation to said section of the result vector of said application step and the value of the state vector of previous iteration.
4. A cryptographic method according to claim 1, wherein said provisional vector and the permutation key are of a same size and are equal to the first intermediate vector's size.
5. Use of a cryptographic method according to claim 1 to generate a pseudorandom data sequence in a method of cryptographically hashing a message to generate a digest of said message, said message including a predetermined number M of data blocks each used in turn as input blocks during successive iterations of the cryptographic method of generating a pseudorandom data sequence to generate M values of the state vector, said digest of said message being obtained from a latest generated value of the state vector.
6. A computer memory device having a computer program stored therein, the computer program including program code instructions for executing the cryptographic hashing method according to claim 5 when said program is loaded into and executed in a computer or a data processing system.
7. A method of encrypting an input data sequence, in which, from an initial value of a state vector of size k and a succession of input words forming said input data sequence, there is generated iteratively a succession of values of the state vector in accordance with the cryptographic method of claim 1 and a succession of output words, each iteration being accomplished by a central processing unit and including:
 an encryption step in which a current output word for said iteration is calculated by a reversible application depending on a current input word and a value of the state vector generated in a previous iteration; and
 a pseudorandom generation step in which a current value of the state vector for said iteration is calculated by a noninvertible application depending at least on said value of the state vector of previous iteration;
 and wherein:
 said reversible application includes at least first and second secret key functions, said secret keys being generated from at least one section of the value of the state vector of previous iteration; and
 said noninvertible application further depends on a current intermediate value, said current intermediate value depending on the value of the state vector of previous iteration and on the current input word, and being isolated from the input words, and from the output words, by means of said first secret key function and said second secret key function.
8. An encryption method according to claim 7, wherein one or both of said first and second secret key functions includes at least one exclusiveOR operation with parameters set by at least one section of the secret key of that function.
9. An encryption method according to claim 7, wherein said provisional vector includes the vector obtained by complementing to 1 each bit of the first intermediate vector.
10. An encryption method according to claim 7, wherein the current value of the state vector is the result of an exclusiveOR operation applied to said section of the result vector of said application step and the value of the state vector of previous iteration.
11. An encryption method according to claim 7, wherein at least one of the input words and the output words includes a number (w) of bits variable as a function of the iteration and the state vector includes a section indicating said number of bits variable in each iteration.
12. An encryption method according to claim 11, wherein the pseudorandom generation step of each iteration further includes, when it is determined from the current value of the state vector that said variable number of bits is zero, calculating a new current value of the state vector, replacing said current value of the state vector, by a noninvertible application depending on said current value of the state vector.
13. An encryption method according to claim 7, wherein:
 said pseudorandom generation step is a first pseudorandom generation step forming a current value of a first state vector;
 said first pseudorandom generation step is combined in parallel with at least one second pseudorandom generation step forming a current value of a second state vector; and
 the current value of the state vector is the result of applying an exclusiveOR operation to the current value of the first state vector and at least the current value of the second state vector.
14. An encryption method according to claim 7, wherein said encryption step is a first encryption step in which there are calculated:
 a first current output word by a first reversible application depending on a first current input word and at least one first section of the value of the state vector of previous iteration; and
 a first current intermediate value; and
 said method further including at least one second encryption step in which there are calculated:
 a second current output word according to a second reversible application depending on a second current input word and at least one second section of the value of the state vector of previous iteration; and
 a second current intermediate value;
 said current intermediate value used during the pseudorandom generation step including said first current intermediate value and at least said second current intermediate value.
15. An encryption method according to claim 14, further including a step of cryptographically multiplexing at least two message blocks to be encrypted to form at least two encrypted message blocks, each message block to be encrypted corresponding to a succession of input words, and wherein said at least two encrypted message blocks are ordered in each iteration as a function of a section of the value of the state vector of previous iteration.
16. An encryption device for encrypting an input data sequence in accordance with the method of claim 7, and generating iteratively from an initial value of a state vector and a succession of input words forming said input sequence, a succession of values of the state vector, and a succession of output words, said encryption device using in each iteration:
 encryption means adapted to calculate a current output word for said iteration by a reversible application depending on a current input word and a value of the state vector generated in a previous iteration; and
 a pseudorandom generator adapted to calculate a current value of the state vector for said iteration by a noninvertible application depending at least on the value of the state vector of previous iteration;
 and wherein:
 said reversible application includes at least first and second secret key functions, the secret keys being generated from at least one section of the value of the state vector of previous iteration; and
 said noninvertible application further depends on a current intermediate value, said current intermediate value depending on the value of the state vector of previous iteration and on the current input word, and being isolated from the input words, and from the output words, by means of said first secret key function and said second secret key function.
17. An encryption device according to claim 16, wherein said pseudorandom generator is a cryptographic generator for generating a pseudorandom data sequence.
18. An encryption device according to claim 16 adapted to process at least one of input words and output words comprising a number of bits variable as a function of the iteration, said device further including means for determining said variable number of bits in each iteration from a section of the state vector and said pseudorandom generator further including means for calculating a new current value of the state vector replacing said current value of the state vector by a noninvertible application depending on said current value of the state vector when it is determined from the current value of the state vector that said variable number of bits is zero.
19. An encryption device according to claim 16, further including a device for cryptographically multiplexing at least two message blocks in clear to form at least two encrypted message blocks, each message block in clear corresponding to a succession of input words, and wherein said at least two encrypted message blocks are ordered in each iteration as a function of a section of the preceding value of the state vector.
20. A computer memory device having a computer program stored therein, the computer program including program code instructions for executing the encryption method according to claim 7 when said program is loaded into and executed in a computer or a data processing system.
21. A computer memory device having a computer program stored therein, the computer program including program code instructions for executing the method of generating a pseudorandom data sequence according to claim 1 when said program is loaded into and executed in a computer or a data processing system.
22. A cryptographic generator of a pseudorandom data sequence formed of a succession of values of a state vector of size k generated iteratively from an initial value of the state vector, said generator including means for using in each iteration to generate a current value of the state vector for said iteration:
 means for obtaining a current intermediate value calculated from a preceding value of the state vector generated in a previous iteration;
 means for forming a permutation key of predetermined size d by selecting d bits from a first intermediate vector of size k, wherein d is less than or equal to k and the first intermediate vector is formed from the preceding value of the state vector in which a section has been replaced by the current intermediate value;
 means for associating with each bit of the permutation key a permutation of size k1 chosen as a function at least of the value of that bit;
 means for applying successively to the input vector the d permutations of size k1 to a provisional vector of size k1 to determine a result vector, wherein k1 is greater than or equal to k and the provisional vector includes the first intermediate vector; and
 means for determining the current value of the state vector from at least one section of the result vector.
23. A cryptographic hashing device generating a digest from a message including a predetermined number M of data blocks, said hashing device including:
 a cryptographic generator according to claim 22, generating a succession of M values of a state vector in M successive iterations; and
 means for, in each of the M iterations:
 calculating the current intermediate value for that iteration from a current data block of the message and the value of the state vector of previous iteration generated by said cryptographic generator; and
 supplying said current intermediate value to the cryptographic generator;
 means for obtaining said digest from a latest value of the state vector generated by said generator.
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Patent History
Type: Grant
Filed: Jun 4, 2008
Date of Patent: Sep 16, 2014
Patent Publication Number: 20100142705
Assignee: Oridao (MontpellierCedex 2)
Inventor: Nicolas Reffe (Montpellier)
Primary Examiner: Linglan Edwards
Application Number: 12/602,626
Classifications
International Classification: H04L 9/22 (20060101); H04L 9/28 (20060101); H04L 9/06 (20060101);